Shouldn't this be accepted also when using "she" instead of "he"?
Both are accepted.
In other examples the response is simply "yes". That was not accepted this time. Why?
There was a typo in the system. And, yes, I'm embarrassed. I've fixed it now and the system will adopt my edit in a week or two. :|
This shows that piha(a) is a new word (it's yellow), but it isn't.
Does it anyhow change the meaning of the sentence (besides of the present simple/continuous) when I use: "Does (s)he clean the yard? Yes, (s)he does." ? Why is not the second option correct? Thank you for explaining.
Yes, it does. The object would be in the accusative for that one: Siivoaako hän pihan?. What English does with verbs, Finnish does with nouns. :)